Question

For an LCR series circuit at resonance, the incorrect statement is

• A. Power factor becomes one
• B. The phase angle between voltages across resistor and source is \(90^\circ\)
• C. Power dissipation is maximum
• D. Impedance is minimum

Hint:

At resonance in a series LCR circuit, \[ \boxed{ X_L=X_C,\qquad Z=R. } \] Therefore, \[ \boxed{ \phi=0^\circ,\qquad \text{Power factor}=1,\qquad I_{\max},\qquad P_{\max}. } \]

Answer 1

The Correct Option is B

Step 1: Recall the conditions at resonance. For a series LCR circuit at resonance, \[ X_L=X_C. \] Hence, the net reactance becomes zero. Therefore, \[ Z=R, \] which is the minimum possible impedance.

Step 2: State the important properties at resonance. At resonance, \[ \boxed{\text{Power factor}=1,} \] since voltage and current are in phase. Also, \[ \boxed{\text{Power dissipation is maximum}} \] because the current is maximum. Further, \[ \boxed{\text{Impedance is minimum}.} \]

Step 3: Identify the incorrect statement. The voltage across the resistor is always in phase with the current. At resonance, the source voltage is also in phase with the current. Hence, \[ \boxed{\text{The phase angle between the resistor voltage and the source voltage is }0^\circ,} \] not \[ 90^\circ. \] Therefore, the statement \[ \boxed{\text{``The phase angle between voltages across resistor and source is }90^\circ\text{''}} \] is incorrect. Hence, the correct option is \(\boxed{(B)}\).